Reflexive properties of rings determined by idempotents
UDC 512.5 We study the reflexive properties of rings determined by idempotents in a more general setting. А new concept named right $e$-reflexive rings is defined and studied. This is a generalization of reflexive rings and right $e$-reversible rings. Some necessary examples and counterexamples are...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8537 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513152420020224 |
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| author | Zhao, Liang Li, Xiaojie Zhao, Liang Li, Xiaojie |
| author_facet | Zhao, Liang Li, Xiaojie Zhao, Liang Li, Xiaojie |
| author_sort | Zhao, Liang |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:39:44Z |
| description | UDC 512.5
We study the reflexive properties of rings determined by idempotents in a more general setting. А new concept named right $e$-reflexive rings is defined and studied. This is a generalization of reflexive rings and right $e$-reversible rings. Some necessary examples and counterexamples are given. Furthermore, we consider the restriction of the right $e$-reflexivity to nilpotent elements, which strictly contains the classes of reflexive rings and right $e$-reflexive rings. Some well-known results on reflexive rings are unified and extended. |
| doi_str_mv | 10.3842/umzh.v77i6.8537 |
| first_indexed | 2026-03-24T03:40:08Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8537 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:40:08Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-85372026-03-21T13:39:44Z Reflexive properties of rings determined by idempotents Reflexive properties of rings determined by idempotents Zhao, Liang Li, Xiaojie Zhao, Liang Li, Xiaojie right e-reflexive ring; right e-reduced ring; right e-reversible ring algebra UDC 512.5 We study the reflexive properties of rings determined by idempotents in a more general setting. А new concept named right $e$-reflexive rings is defined and studied. This is a generalization of reflexive rings and right $e$-reversible rings. Some necessary examples and counterexamples are given. Furthermore, we consider the restriction of the right $e$-reflexivity to nilpotent elements, which strictly contains the classes of reflexive rings and right $e$-reflexive rings. Some well-known results on reflexive rings are unified and extended. УДК 512.5 Рефлексивні властивості кілець, що визначені ідемпотентами Досліджено рефлексивні властивості кілець, визначених за допомогою ідемпотентів у більш загальному контексті. Введено та вивчено нове поняття – праве $e$-рефлексивне кільце, що є узагальненням рефлексивних і правих $e$-реверсивних кілець. Наведено відповідні приклади та контрприклади. Крім того, досліджено обмеження правої $e$-рефлексивності на нільпотентні елементи, що строго містить класи рефлексивних і правих $e$-рефлексивних кілець. Узагальнено та об’єднано деякі відомі результати про рефлексивні кільця. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8537 10.3842/umzh.v77i6.8537 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 6 (2025); 447–448 Український математичний журнал; Том 77 № 6 (2025); 447–448 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8537/10538 Copyright (c) 2025 Liang Zhao, Xiaojie Li |
| spellingShingle | Zhao, Liang Li, Xiaojie Zhao, Liang Li, Xiaojie Reflexive properties of rings determined by idempotents |
| title | Reflexive properties of rings determined by idempotents |
| title_alt | Reflexive properties of rings determined by idempotents |
| title_full | Reflexive properties of rings determined by idempotents |
| title_fullStr | Reflexive properties of rings determined by idempotents |
| title_full_unstemmed | Reflexive properties of rings determined by idempotents |
| title_short | Reflexive properties of rings determined by idempotents |
| title_sort | reflexive properties of rings determined by idempotents |
| topic_facet | right e-reflexive ring right e-reduced ring right e-reversible ring algebra |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8537 |
| work_keys_str_mv | AT zhaoliang reflexivepropertiesofringsdeterminedbyidempotents AT lixiaojie reflexivepropertiesofringsdeterminedbyidempotents AT zhaoliang reflexivepropertiesofringsdeterminedbyidempotents AT lixiaojie reflexivepropertiesofringsdeterminedbyidempotents |